is the collection of all real-valued
continuous functions defined on some interval 
. 
is the collection of all functions 
with continuous 
th derivatives. A function space
is a topological vector space whose "points"
are functions.
See also
Functional, Functional Analysis, Operator
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Cite this as:
Weisstein, Eric W. "Function Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FunctionSpace.html